A curve, with an eccentricity equal to 1, obtained by slicing a cone with a plane parallel to one side of the cone. A parabola can be considered an ellipse with an infinite major axis. It is one of the types of conic section.
One of the most studied curves in the history of mathematics, a parabola is the outline of the figure obtained if a right circular cone is cut by a plane that is exactly parallel to the cone's side. Just as the circle is a limiting case of the ellipse when the two foci coincide, the parabola is a limiting case of the ellipse when one of the foci is moved to infinity. As the French mathematician Henri Fabre eloquently put it, that parabola is an ellipse that "seeks in vain for its second, lost center." Johannes Kepler drew this further connection between the parabola and other conic sections:
Because of its intermediate nature the parabola occupies a middle position [between the ellipse and the hyperbola]. As it is produced it does not spread out its arms like the hyperbola but contracts them and brings them nearer to parallel, always encompassing more, yet always striving for less – whereas the hyperbola, the more it encompasses, the more it tries to obtain.
Euclid dealt with the parabola in his Conic Sections, and, although this treatise was lost, it provided a foundation for the first four books by Apollonius of the same name. Galileo discovered that a cannonball, or any other projectile launched at an angle to ground, follows a parabolic path: a result that immediately grabbed the attention not only scientists but of monarchs and military leaders. René Descartes, in writing La Géométrie (1637), chose the parabola to illustrate his innovative analytical geometry. In 1992, Rudolph Marcus of the California Institute of Technology won the Nobel Prize in Chemistry for his work showing that parabolic reaction surfaces can be used to calculate how fast electrons travel in molecules. His most famous theoretical result, an inverted rate-energy parabola, predicts electron transfer will slow down at very high reaction free energies.
Related categories PLANE CURVES
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